A B-group is an analytically finite Kleinian group with a simply connected invariant component. We divide the non-elementary B-groups into three classes: Fuchsian and quasifuchsian groups (these are groups with exactly two components, both invariant), degenerate groups (these are groups with exactly one component), and groups that contain accidental parabolic transformations. We also demonstrate the existence of degenerate groups, and discuss the structure of groups containing accidental parabolic transformations.
KeywordsStructure Loop Kleinian Group Fuchsian Group Simple Loop Simple Closed Curve
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